THE ECONOMIC COST OF GENDER DISCRIMINATION IN THE BRAZILIAN LABOUR

MARKET

Abstract:

Gender discrimination in the labor market can take several forms, creating wage differentials that are

unrelated to productivity. The existence of these differences implies an economic cost for the economy in

terms of production and labor income. In this article, these losses were estimated through the interaction of

wage decomposition models and simulations with an input-output model. The wage decomposition was

calculated at different points of the income distribution, using the recentered influence function (RIF)

developed by Firpo et al. (2009). Using the results of the decomposition, it was possible to calculate

individual wages adjustments, following steps proposed by Oaxaca and Ranson (2003), so that all individuals

are remunerated according to their observable characteristics as well as the non-discriminated group. In turn,

these estimates were used to compile two vectors of shock, for the simulation of rising nominal costs of

labor, and consumption, considering households divided by income deciles. The wage decomposition model

was estimated using the National Household Survey (from Portuguese PNAD – Pesquisa Nacional por

Amostra de Domicílios) for 2013. The input-output matrix estimate was based on the supply and use tables

for 2013, according to the procedures described in Guilhoto and Sesso Filho (2005) and the hypothesis of

"industry-based" technology. The first simulation operates basically as the following: i) the adjustment was

calculated at the individual level, ii) the change in sectorial labor cost depends on the total adjustment owed

to all women working in that sector; iii) the increase in wages is incorporated as a rise in production cost, that

causes expanding prices; iv) using Leontief price model assumptions, if the amount of money in the economy

is the same, final demand is adjusted and the production falls; v) employment follows production. In the

second simulation, it was assumed that the economy changed due to the first shock. Therefore, using the

updated Leontief matrix, it was applied a second shock increasing consumption for all households, according

to the income rise in each decile calculated at individual level and aggregated by income decile.

Consequently, in the second simulation, consumption increases production; and employment follows

production. The simulation results indicate that the income effect generated through consumption overcomes

the price effect, due to the wage rising in terms of production and welfare but not in terms of employment.

Nonetheless, the results are very heterogeneous across sectors and households.

Key-words: discrimination, women, wage decomposition, input-output simulation

JEL Classification: J7, C21, C67

1. INTRODUCTION

Discrimination in the labor market has received particular attention among researchers. As Cain (1984)

argues, wages are the most important source of income that people can earn by their own effort, making the

labor market an important mechanism of social distribution, with important consequences on inequality

(VEMMAN, 2010). In this regard, Brazil is a prominent example. In particular, since the early 2000s, the

country has adopted social policies that aimed to reduce income inequalities and foster social inclusion.

Examples are the “Bolsa Família” program, and other initiatives, such as “Brasil Carinhoso” and “Brasil sem

Miséria” (PORTAL BRASIL, 2013). While these policies have generated results that are positive in

aggregate, research has been lacking on their contribution to the reduction of current levels of inequality.

Gender discrimination is one those factors, as it generates significant and persistent wage gaps

(CAIN, 1999), through which many forms of discrimination are associated with poverty (CAMBOTA and

MARINHO, 2006). In this way, the labor market at the same time reveals and generates inequalities

(BARROS, et al., 2006). As a consequence, individuals discriminated against are concentrated in the bottom

part of the income distribution, in the poorest regions, and having limited opportunities for social

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advancement. These happens not only directly due to discrimination, but also by reduced access to

educational and professional training (CAMBOTA and MARINHO, 2006; GUIMARÃES, 2006; GRADÍN,

2009).

Even so, income differences cannot be directly taken as evidence of discrimination (HECKMAN,

1998; BLANK et al., 2004), since they constitute the result of a set of factors and disparities in the labor

market (BLANK et al., 2004). Each group has its own economically relevant characteristics that are valued

differently in the market and directly explain the differences in labor earnings (STIGLITZ, 1973). In this

sense, there is discrimination in the labor market when equally productive individuals are evaluated

differently based on nonproductive aspects, such as race and gender (BECKER, 1971, ARROW, 1973).

From a neoclassical economic theory perspective, the great challenge, according to Cohn (2000), was

responding to the major paradox of discrimination: after all, if firms are fully rational, gender and race

discrimination could not exist. More than that, if equally productive individuals do not receive the same

wages, there must be some market failure, such as information asymmetry, or other mechanisms that act

directly on the wage determination and which cannot be directly explained by traditional models.

Such questions supported the development of the literature of economic discrimination, from Becker

(1971) with his definitions of tastes and preferences for discrimination, towards Phelps (1972) and Arrow

(1973). The last two authors created the concept of statistical discrimination, giving certain rationality in

determining discriminatory wages. For them, wage differentiation over groups would be a direct consequence

of asymmetric information in the labor market with respect to qualifications and investments in human

capital.

Notwithstanding the development of an extensive literature on these theoretical models, it has proven

very difficult to test them empirically, mainly due to lack of data. Even with more detailed data sets, it

remains difficult to determine the exact nature of discrimination (ALTONJI and BLANK, 1999). In practice,

according to O'Neill and O'Neill (2005), the distinction between statistical discrimination derived from

prejudice and discrimination is far from straightforward, since none of the theories of discrimination in the

labor market is satisfactory to explain all the variation observed wage differentials in society (CAIN, 1984;

O'NEILL and O'NEILL, 2005; LANG and LEHMANN, 2011).

For these reasons, researchers, according to O'Neill and O'Neill (2005), attempted to explore broader

issues that can be directly measured. Therefore, the empirical literature has been more targeted to test

whether there is discrimination, than to test specific theoretical models (FANG and MORO, 2011).

In this context, the decomposition of wages, suggested by Blinder (1973) and Oaxaca (1973), are the

most widely used methods to measure discrimination in the labor market, and can be applied even without

data specifically designed for discrimination analysis. In these models, given the concept of discrimination in

the labor market, the wage differential between groups can be explained mainly by two factors: changes in

the distribution of observable characteristics, and discrimination. Accordingly, the method determines to

what extent wage differentials are indeed differences in productivity or are related to other factors.

At first, the decomposition methods were concentrated on measuring discrimination in average wages

between groups. However, some authors have observed that the effect of the covariates may not be constant

along the distribution (MACHADO and MATA, 2005), and wage inequality can be explained by changes in

observed variables with specific implications for particular points along the income distribution (FORTIN et

al, 2011). Nevertheless, the methodological refinements later developed, some questions remain open: What

are the consequences of gender and race discrimination for households’ welfare? What are the consequences

for the economy as a whole?

According to D’Amico (1987), discrimination incurs a cost to society, inevitably leading to an

efficiency loss due to underutilization of productive resources that further discourage human capital

investment. In this sense, the discrimination produces a loss of productivity, and consequently the level of

production falls below its potential. To clarify these issues, it is necessary to explain the connections between

the decisions of individuals and firms, and the inclusion of these in the productive system. From the

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individual perspective, discrimination negatively affects decisions directly related to the labor market, like

investment in human capital, occupational choice and job supply itself, but also has a negative impact on

consumption. On the other hand, from the perspective of firms, although the equalization of wages is usually

seen as a cost, the indirect effects of discrimination on the labor supply and demand counteracts the cost.

In order to capture some of these effects, this paper proposes a bottom-up integration between a micro

model of wage discrimination and an input-output model. At the micro level (individual), the first step was to

calculate the wage a woman should receive if there was no gender discrimination in Brazilian labor market,

and in the second step these values were used in two complementary shocks in an input-output model. In the

first step, we calculated the effect of rising wages over sectorial prices, using a Leontief price model,

secondly, we calculated the effect on consumption.

The paper is divided as follows: the next section briefly describes general aspects of the empirical

literature, while section three describes the methodology used, including the wages decomposition, the wage

adjustment method proposed by Oaxaca and Regan (2003), and the proposed simulations using input-output

analysis. Section four shows the results and, the final section describes some final remarks.

2. EMPIRICAL LITERATURE

In the empirical literature, it is possible to identify several studies conducted using Brazilian data. These

studies range from direct applications of the Blinder and Oaxaca method, as in Leme and Wajnman (2000);

Campante et al. (2004); Gilberti and Menezes-Filho (2005), Kings and Crespo (2005), Guimarães (2006);

Matos and Machado (2006) and Cacciamali et al. (2009), as well as some methodological extensions, for

instance, Arcand and D'Hombres (2004) and Milk (2005). For the surveyed literature, the database used was

PNAD, with applications for several years. Moving forward to decompositions along the distribution, notable

studies are those of Smith (2000), Guimarães (2004); Crankshaft and Marino (2005), Oliveira and Rios-Neto

(2006); Bartalotti and Biderman (2007) Silver (2009), Coelho et al (2010) and Arraes et al.,2014).

Overall, there are some regularities. When compared to the group of white men, the wage differential

for white women is a result of discrimination in the labor market, i.e., the result of unobserved factors that

lead to low return from their observed characteristics. In turn, the gap for black men is a result of pre-market

discrimination, resulting in lower levels of education and/or qualification. Finally, and as expected, the case

of black women combines the previous two cases (SOARES, 2000; BIDERMAN and GUIMARÃES, 2004;

BARTALLOTI, 2007; CAMBOTA and MARINHO, 2005; CACCIAMALI et al., 2009).

In the international literature, there are several applications of methods involving quantile regressions;

they reinforce the existence of a relationship between wage differentials and social mobility, showing that

discrimination not only has different impacts at different points of the distribution, but also increases with the

wage level. This behavior is known as "glass ceiling,"1 and was observed for Brazil in Campante et al.

(2004); Gilberti and Menezes-Filho (2005) Milk (2005); Bartalotti (2007); Cacciamali et al. (2009); Prata

(2009) and Coelho et al. (2010), for Colombia in Badel and Penha (2010), to the United States in

Kassenböhmer and Sinning (2010), to Australia in Kee (2006) and to Europe in Albrecht et al. (2003, 2009),

Arulampalam et al. (2007) and de la Rica et al. (2008), among others.

In turn, when the wage gap is larger at the beginning of the distribution, it can be said that there is a

"sticky floor" preventing people from moving forward, as noted by Arulampalam et al. (2007) for Spain

(between fifty and tenth percentile, and between the twenty-fifth and tenth percentile) and Italy (only

between the fiftieth and tenth percentile), and De la Rica et al. (2008) for low-skilled workers in Spain.

Although the main advantage of the method is the possibility of application in the absence of specific

data on discrimination according to Altonji and Blank (1999), even if the decompositions are consistent with

1 Campante et al (2004) defines the glass ceiling as an "elitist profile" of the wage distribution.

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the hypothesis of the presence of discrimination, a few methodological caveats are necessary: i) model

specification (as a predictor of individual wages), ii) measurement errors, and iii) omitted variables.

First, it is necessary to include a complex set of attributes relating wages to individual’s productivity,

which in practice is not available (GUIMARÃES, 2006). There are several variables that affect the wages but

cannot be captured by more general research, as in the case of PNAD. As a result, the variables usually used

as a proxy for productivity are full of measurement errors, at the same time other variables that could affect

wages are not available (GUIMARÃES, 2006).

The specification problem is directly related to the complexity of wage determination. According to

Figueiredo and Silva (2012), part of the income is determined by a set of effort variables (such as educational

level, the decision to migrate and hours worked per year). On the other hand, another part is determined by

factors over which the individual does not have control, but that indirectly affect their choices, called

situational variables (such as level of parents’ education and occupation, race, gender, age, and birth region).

In this way, the results are limited to the proxies provided by surveys, which are subject to specification

errors.

Even with all possible control variables, according to Darity and Mason (1998), Altonji and Blank

(1999) and Tomaskovic-Devey et al. (2005) discrimination affects investments in human capital (and other

pre-labor market features) leading to underestimation of discrimination, as any variable investment in human

capital carries a component of pre-market discrimination. Therefore, the model will inevitably be subject to

an omitted variables bias related to human capital decisions, and individual preferences, which are correlated

with wages and may overestimate or underestimate the differential unexplained (HECKMAN, 1998;

ALTONJI and BLANK, 1999; BLANK et al., 2004).

In this regard, as suggested by Blank et al. (2004), it will always be difficult to argue that any set of

variables chosen to explain wages is a complete set of variables related to worker productivity. Therefore,

given the data available, following the advice of Guimarães (2006), the researcher must specify the model as

fully as possible and interpret the results with caution. Doing so, the wage decompositions can be an

important tool to understand what factors are related to observable characteristics that determine wages and

its variations, while measuring the magnitude of the differences that cannot be explained by these attributes

(BLANK et al., 2004).

3. METHODOLOGY

Schematically, the interconnection between the wage decomposition model and the input-output simulation

can be seen in Figure 1. From the results of the decomposition (at different points of the income distribution,

calculated using the methodology of Firpo et al. (2009) it was possible to calculate individual wages

adjustments, following steps proposed by Oaxaca and Ranson (2003), so that all individuals are now

remunerated according to their observable characteristics as well as the non-discriminated group (white

men). In turn, these estimates were used to compile the vectors of shock, for the simulation of rising nominal

costs of labor, and consumption. The following sections discuss each method in particular.

The wage decomposition model was estimated using the National Household Survey (from

Portuguese PNAD – Pesquisa Nacional por Amostra de Domicílios) for 2013 (IBGE, 2016a). The input-

output matrix estimate was based on the supply and use tables of the Brazilian Institute of Geography and

Statistics (IBGE) for 2013, according to the procedures described in Guilhoto and Sesso Filho (2005) and the

hypothesis of "industry-based" technology (Miller and Blair, 2009). The household consumption

disaggregation into different income deciles was made from data in the Household Budget Survey (IBGE,

5

2016b), while labor incomes were disaggregated according to data from the National Household Sample

Survey (PNAD).

3.1. Wage Decomposition and Adjustment

For this paper, we used the recentered influence function (RIF) developed by Firpo et al. (2009)2. An

extensive discussion and comparisons between different types of wage decomposition methodologies can be

seen in Fortin et al. (2011). The methodology facilitated the estimation of different wage equations for ten

income deciles. Therefore, it is possible to estimate how much of the wage differentials between men and

women could be attributed to explained (productivity related) factors, and how much could be only explained

by labor market discrimination.

To determine the monetary value that each individual ought to receive in the absence of

discrimination in the labor market, Oaxaca and Ranson (2003) discuss several possibilities using the Blinder-

Oaxaca decomposition, which we modified to be applied in the quantile decomposition results, as follows. If

group 𝐵 is discriminated against, each individual of this group ought to receive a wage based on the wage

equation of group 𝐴 (non-discriminated). Hence, for each individual 𝑖 in quantile 𝜏3:

�̂�𝑖𝐵𝐴 = ∑ 𝑋𝐵𝑖𝑘�̂�𝐴𝑘

𝐾

𝑘=1

(1)

where �̂�𝑖𝐵𝐴 is the estimated wage for individual 𝑖 from group 𝐵, using the wage equation coefficients for group

𝐴. 𝑋𝐵𝑖𝑘 are 𝑘 observed characteristics for individual 𝑖 from group 𝐴 and 𝛾𝐴𝑘 represent the estimated coefficients for 𝑘 variables of group 𝐴. Thus, the wage differential predicted for each woman in Group 𝐵 (discriminated) is given by:

𝑒𝑖𝐵𝐴 = 𝑌𝐵𝑖 − �̂�𝑖𝐵

𝐴 (2)

where 𝑌𝐵𝑖 is the observed labor income. For Oaxaca and Ranson (2003) the naïve approach is to define the adjustment as predicted by equation (2):

𝐴𝐵𝑖(1)

= − 𝑒𝑖𝐵𝐴 (3)

where 𝐴𝐵𝑖(1)

is the necessary wage adjust for each 𝑖, belonging to group 𝐵. Thus, if group 𝐵 has 𝑁𝐵 individuals, the aggregated adjustment is:

𝐴𝐵(1) = ∑ 𝐴𝐵𝑖

(1)

𝑁𝐵

𝑖=1

= ∑ − 𝑒𝑖𝐵𝐴

𝑁𝐵

𝑖=1

= 𝑁𝐵�̂� (4)

where �̂� is the average wage adjustment for group 𝐵, which implies an average adjusted wage for each individual belonging to group 𝐵 equivalent to:

�̂�𝐵𝐴 = �̅�𝐵 + �̂� (5)

The methodology corresponds to bringing all individuals to the hyperplane of estimated wages

regression for the non-discriminated group. However, errors predicted for the non-discriminated group would

cause an asymmetry, as the wage equation estimated is not a perfect predictor of individual wages. In this

case, the adjustment would lead to differences in payments not only in the group discriminated against, but

also in the reference group.

To correct this asymmetry, Oaxaca and Ranson (2003) proposed an alternative estimation where the

predicted error for each individual (on its own wages regression) is incorporated into the adjustment. That is,

2 For all regression we used Mills’ ratio to correct for selective bias in labor market participation. 3 The quantile indicator (𝜏) was omitted to simplify the notation.

6

it is assumed that the portion of individual wages not predicted by the wage equation of each group is due to

individual characteristics, unmeasured, and randomly distributed, such as work motivation and innate skills,

which remain with the individual even after the adjustment. Therefore, the new adjustment is given by:

𝐴𝐵𝑖(2)

= 𝐴𝐵𝑖(1)

+ 𝑒𝑖𝐵𝐵 = −𝑒𝑖𝐵

𝐴 + 𝑒𝑖𝐵𝐵 = �̂�𝐵

𝐴 − �̂�𝐵𝐵 (6)

Thus, the adjustment becomes equivalent to the difference between the predicted earnings for group

B, using the equation of group A, minus group B own wages prediction. In aggregate terms:

𝐴𝐵(2)

= ∑(−𝑒𝑖𝐵𝐴 + 𝑒𝑖𝐵

𝐵 )

𝑁𝐵

𝑖=1

= 𝐴𝐵(2)

(7)

According to the assumptions of the OLS estimator: − ∑ 𝑒𝑖𝐵𝐴 = 0

𝑁𝐵𝑖=1 ; hence, the total adjusting cost

for employers is exactly the same, however, the individual adjustment distribution changes. In this case, the

non-discriminated adjustment (group 𝐴) would be zero, because: 𝐴𝐴𝑖(2)

= �̂�𝐴𝐴 − �̂�𝐴

𝐴 = 0. Although the second adjustment proposal solves the asymmetry problem between groups, there is no

guarantee that all discriminated individuals maintain or improve their wages. This happens because it is

possible for < 0 for discriminated individuals whose wages predicted by the equation of non-discriminated group is lower than the observed wage, which would imply a wage reduction for some individuals of group

𝐵. As the authors note, the implementation of such adjustment would not be possible for legal reasons, which forbid wage reduction. To solve the problem, it is necessary to restrict the compensation only to individuals

with adjusted salary higher than the observed one, i.e.:

𝐴𝐵𝑖(3)

= 𝜙𝐵𝑖𝐴𝐵𝑖(2)

𝜙𝐵𝑖 = {1 𝑠𝑒 𝐴𝐵𝑖

(2)> 0

0 𝑠𝑒 𝐴𝐵𝑖(2)

≤ 0

(8)

However, in this case, the total cost is greater than the value predicted by the decomposition model,

over-compensating the discriminated group, and burdening the firms more than necessary. Once again, to fix

this problem, Oaxaca and Ranson (2003) propose the redistribution of initial adjustment (𝐴𝐵(1) = 𝐴𝐵

(2) =

𝑁𝐵𝐷 ̂ ) according the share of each individual whose salary is below the estimated (𝜙𝐵𝑖 = 1) in the total

positive adjustment (𝐴𝐵(3)

). Therefore, the participation of each individual discriminated against in the

adjustment is:

𝜆𝐵𝑖 =𝐴𝐵𝑖

(3)

𝐴𝐵(3)

=𝜙𝐵𝑖𝐴𝐵𝑖

(2)

𝐴𝐵(3)

(9)

such that:

0 ≤ 𝜆𝐵𝑖 ≤ 1

∑ 𝜆𝐵𝑖

𝑁𝐵

𝑖=1

= 1 (10)

The adjustment can be defined as:

𝐴𝐵𝑖(4)

= 𝜆𝐵𝑖𝐴𝐵𝑖(2)

(11)

All individuals effectively discriminated (𝜙𝐵𝑖 = 1) receive some wage adjustment, while the total amount of the adjustment (which must be paid by firms) would be exactly the amount of the discrimination

coefficient estimated by the wages decomposition.

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In this paper, for each income decile it was necessary to define a criterion for an individual 𝑖 belonging to group 𝐵, whose observed wage salary is 𝑌𝑖, to receive an adjustment of wage (𝐴𝐵𝑖,𝜏) corresponding to the prediction for quantile 𝜏. Accordingly, defining 𝜅𝑡 as a quantile for which de decomposition was calculated, such as 𝜅𝑡 = 𝜅1, … , 𝜅𝑇, and when 𝜅𝑡 = 𝜅𝑇, 𝑞𝜏 = 1; the wage adjustment for each 𝑖, located in the 𝜏-th quantile, is represented by:

𝐴𝐵𝑖,𝜏 = 𝜓𝐵𝑖,𝜏𝐴𝐵𝑖,𝜅𝑡

𝜓𝐵𝑖,𝜏 = {𝐴𝐵𝑖,𝜅1 , se 𝜏 ≤ 𝜅1

𝐴𝐵𝑖,𝜅𝑡 , se 𝜅𝑡−1 < 𝜏 < 𝜅𝑡

(12)

In this way, if the recentered influence function was calculated to each decile of wage distribution, so

the individuals, for example, in the tenth percentile should receive the adjustment calculated for the first

decile; the workers between the tenth and twentieth percentiles should receive the adjustment calculated for

the second decile, and so on.

Consequently, the average adjustment to 𝜏 as defined by (11), must be the same as calculated in the wage decomposition for the whole distribution. However, only some share receives this adjustment, and it is

not possible to guarantee that the average adjustment is equal to the total predicted for the whole distribution.

To make sure that this occurs, a new criterion for adjustment, similar to the ones proposed before, is made:

𝐴𝐵,𝜅(5)

= ∑ 𝐴𝐵𝑖,𝜅(5)

= 𝑁𝐵,𝜅�̂�𝜅

𝑁𝐵,𝜅

𝑖=1

(13)

where 𝑁𝐵,𝜅 is the number of individuals in group 𝐵 who will receive the adjustment calculated for the

𝜅 quantile, and �̂�𝜅 is the average adjustment calculated for the 𝜅 quantile throughout the distribution. Redefining the equation (9) as the participation of each discriminated individual in the adjustment for the 𝜅 quantile:

𝜆𝐵𝑖,𝜅 =𝐴𝐵𝑖,𝜅

(3)

𝐴𝐵,𝜅(3)

(14)

Thus, the received adjustment to each individual in group 𝐵, and quantile 𝜅, using the function 𝜓𝐵𝑖,𝜏 drawn up in (12), is:

𝐴𝐵𝑖,𝜅(5)

= 𝜆𝐵𝑖,𝜅𝐴𝐵,𝜅(5)

= 𝜆𝐵𝑖,𝜅𝑁𝐵,𝜅�̂�𝜅 (15)

It is worth mentioning that some individuals may receive a wage adjustment lower than their own

merits, because they absorb the deficit of those whose adjustment would be negative.

3.2. Input-Output Model

The input output model is a linear system of equations describing the economic system. The basic equation,

according to Miller and Blair (2009), can be expressed as:

𝑥 = 𝑍 + 𝑓 (16)

where 𝑥 is a vector of total output by industry, 𝑍 is the intermediate input matrix that represents the economic flows between industries, and 𝑓 is the vector of final demand by industry. Then, the technical coefficient matrix is given by:

𝐴 = 𝑍�̂�−1 (17)

where each element of 𝐴 = 𝑎𝑖𝑗 shows the amount industry i product used as intermediate input by industry j.

Therefore, the model's solution can be represented as.

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𝑥 = (𝐼 − 𝐴)−1𝑓 (18)

where (𝐼 − 𝐴)−1 is the total impact matrix referred to as the Leontief inverse matrix. In this model, all flows between industries are in monetary terms and prices are fixed at the base year

value. However, to estimate a price effect of the wage adjustment, it is possible to change the production

cost, that is incorporated in output prices, using the Leontief price model (1941, 1946).4 Thus, initially,

industrial output 𝑥 is equal to the sum of inputs cost to the value added 𝑣 components.

𝑥′ = 𝑖′𝐴�̂� + 𝑣′ (19)

Post-multiplying equation (19) by �̂�−1, it follows that:

𝑖′ = 𝑖′𝐴 + 𝑣′�̂�−1 (20)

Yielding 𝐿 = (𝐼 − 𝐴)−1 and assuming that the price is equal to the production cost so that 𝑖′ = 𝑝0, the price index for the base year is given by:

𝑝 = 𝐿′𝑣′�̂�−1 (21)

To impose a wage adjustment, a vector, 𝑇 is defined that is calculated according to value added in this sector as:

𝑇 = 𝜑𝑣 (22)

where 𝜑 is the rate of wage adjustment for each sector. Therefore, using 𝜏 = 𝑇�̂�−1, the adjusted prices vector (𝑝∗) can be calculated as:

𝑝∗ = 𝐿′(𝑣�̂�−1 + 𝜏)𝑝 (23)

Following Gemechu et al. (2014), if the monetary values of sectoral output are held constant, before

and after tax, then the sectoral real output becomes:

𝑥∗ = (𝑝/𝑝∗)𝑥 (24)

Therefore, the impact on the price index (𝜋) is given by:

𝜋 = ∑ 𝑝𝑗∗𝛼𝑗𝑗 (25)

where 𝛼𝑗 is the share which industry 𝑗 production represents in total output. The government revenue with

new tax was estimated as:

𝑅 = 𝜑𝑥∗ (26)

Assuming households maximize their utilities using a Leontief function, and their income and savings

are unchanged, none of each representative household could afford the same basket of goods. Therefore,

using price changes derived from the model, it is possible to calculate the change in consumption as a

measure of welfare. Formally, household welfare change (∆𝑤𝑘) for decile 𝑘 is the following:

∆𝑤𝑘 = (∑ 𝑐𝑖𝑘𝑝

𝑖

) − (∑ 𝑐𝑖𝑘𝑝∗

𝑖

) (27)

where 𝑐𝑖𝑘 is the quantity consumed by decile 𝑘 from industry 𝑖. For the income/consumption effect, equation (18) was used, updated after the price change, and we

shocked the final demand the amount of wage adjustment calculated previously.

4 It is important to highlight, that, according to Miller and Blair (2009), Ghosh model (1958) produce the same results. For

different interpretations of Ghosh and price models, see Dietzenbacher (1997), Oosterhaven (1996) and Mesnard (2009).

9

4. RESULTS

4.1. Wages Decomposition and Adjustment

Wage decompositions have been estimated by deciles5 for individuals between 16 and 65 years. The

dependent variable, hourly wage logarithm in the main job, was regressed with the following controls: age;

age squared; school attendance (dummy); rural and urban region (dummy); years of education (between zero

and three years, four and seven, eight and ten, eleven and fourteen, and more than fifteen); occupation type

(formal, informal, self-employed and employer); family type (couples with and without children; others); and

regional dummies for Federative Unions. All workers employed in the public sector were excluded from the

sample.

The aggregate results divided into the proportion explained by observable characteristics and the

unexplained share indicate effects similar to those reported in the literature reviewed (Table 1).6 The

decomposition showed that for their observed characteristics, women should receive higher wages than those

of men. Nevertheless, women have lower returns to these characteristics increasing the gap in favor of men.

Similar results can be seen in Soares (2000); Biderman and Guimarães (2004); Bartalloti (2007); Cambota

and Marinho, (2005); Cacciamali et al. (2009).

In general, it is possible to highlight three distinct points in the path of wage gap across the

distribution (Figure 2): i) a high discrimination in the first deciles suggesting the effect of "sticky floor"

observed by Arulampalam et al (2007) for Spain and Italy, which can be explained by the informality at the

beginning of the income distribution favoring discrimination; ii) the change of direction around the fourth

decile, may be related to the minimum wage, which equals the income of workers around the value set by the

government and iii) increased discrimination from the fifth decile suggesting the effect of "glass ceiling,"

which reveals the existence of barriers to entry of blacks to positions of higher pay.

Following the methodology proposed by Oaxaca and Ranson (2003) (presented in section 3.1) wage

adjustments were calculated from the recentered regressions. Thus, it was possible to simulate the wage for

women if their payments were obtained based on the remuneration of characteristics for men for each

individual. The necessary adjustment estimated (as adjust five) industry were used as for input-output

simulations.

4.1. Input-Output Simulations

According to the exposition in section 3.2, two simulations were conducted using the input-output model.

The first simulation accounts for the price effect, i.e., the effect of rising production costs through women’s

wages increases. On the other hand, the second simulation focuses on the income effect, generated by

increasing consumption for every decile of income in proportion to the wage adjustment. Sectorial results for

both simulations can be found in Table 2.

The first simulation operates basically as the following: i) the adjustment was calculated at the

individual level, ii) the change in sectorial labor cost depends on the total adjustment owed to all women

5 It was estimated regressions at the points: 0.10; 0.20; 0.30; 0.40; 0.50; 0.60; 0.70. 0.80; 0.90; and 0.99 of the wage distribution. 6 Complete results can be obtained by contacting the authors.

10

working in that sector; iii) the increase in wages is incorporated as a rise in production cost, that causes

expanding prices; iv) using Leontief price model assumptions, if the amount of money in the economy is the

same, all households need to adjust their consumption and the production falls; v) employment follows

production.

In the second simulation, it was assumed that the economy changed due to the first shock; however,

now, women wages are higher and there is a consumption growth proportion to the wage adjustment.

Therefore, there are only three developments: i) consumption increases production; ii) employment follows

production; iii) as a model assumption, prices do not change.

The consumption results for both simulations are the most important in terms of policy (Table 3). For

the first three deciles, the income effect is surpassed by the price effect. For these households, the rise in

prices overcomes the benefit of ending female discrimination. The same happens for the last decile, but not

between deciles four and nine, thus guarantying a positive welfare effect for the economy as a whole. Table 4

summarizes the results for aggregated variables. It shows how the total effect over aggregated production is

positive, even if not for all sectors. The same happens to welfare. The overall effect is positive despite

negative effects for some households. The negative results can be explained by both the rise in prices and the

employment losses.

5. FINAL REMARKS

Discrimination in the labor market imposes a cost on society by penalizing individuals discriminated against

and by reducing the potential output, as suggested by D'Amico (1987). This paper seeks to address these

issues for the Brazilian economy, through the integration of an econometric model of wage decomposition

and input-output simulations. The first model was used to calculate how much women wages should increase

so that there is no discrimination in the labor market. The input-output model was used to simulate the effect

of such a change for the role economy.

The simulation results indicate that the income effect generated through consumption overcomes the

price effect for the economy as a whole, due to the wage rising in terms of production and welfare but not in

terms of employment. Nonetheless, the results are very heterogeneous across sectors and households.

It is worth noting that the results here have several underlying and restrictive assumptions; however,

they constitute what would be the first effect of eliminating gender discrimination in Brazilian labor market,

and they can yield some light on short-run effects. In the long-run, technological changes can be expected to

modify the way sectors combine inputs and generated output, as well as a direct effect over women labor

supply. As the expected wages for women grows up, more women’s labor supply should grow, reinforcing

the positive effect over the income, not to mention the pure effect of been able to work with fair wages.

Another important point to be highlighted is that the simulation was performed only considering

discrimination in the labor market, i.e., given the characteristics individual as fixed. However, as pointed out

by several studies (Cain, 1984; Altonji and Blank, 1999; Blank et al., 2004; Vemman, 2010; Lang and

Lehmann, 2011), these characteristics are influenced by pre-market features, such as investment in education

and qualification, experience and own decision to enter or not in the labor market, issues that have not been

addressed in this work. These and other topics are intended to be part of future developments.

11

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14

Figures:

Figure 1 – Linkage between Wage Decomposition and Input-Output Simulations

Source: Prepared by the authors

Figure 2 – Wage decomposition results in percentage of explained and unexplained differential by decile

Source: Prepared by the authors

-0,30

-0,20

-0,10

0,00

0,10

0,20

0,30

0,40

Explained Difference Unexplained Difference

15

Tables:

Table 1 – Wage decomposition results

Hourly log wage

for men (1)

Hourly log wage

for women (2)

Difference

(1) – (2)

Explained

Difference

Unexplained

Difference

Decile 1 1.140*** 0.957*** 0.182*** -0.0633*** 0.246*** (0.000134) (0.000645) (0.000658) (0.000271) (0.000665)

Decile 2 1.359*** 1.335*** 0.0244*** -0.0118*** 0.0362*** (8.60e-05) (9.67e-05) (0.000129) (0.000209) (0.000223)

Decile 3 1.525*** 1.448*** 0.0761*** 0.00403*** 0.0720*** (0.000129) (5.04e-05) (0.000139) (0.000294) (0.000299)

Decile 4 1.690*** 1.549*** 0.141*** 0.0154*** 0.126*** (0.000197) (0.000129) (0.000235) (0.000421) (0.000433)

Decile 5 1.863*** 1.664*** 0.200*** 0.00752*** 0.192*** (6.81e-05) (0.000146) (0.000161) (0.000141) (0.000188)

Decile 6 2.033*** 1.839*** 0.193*** 0.00202*** 0.191*** (8.75e-05) (7.96e-05) (0.000118) (0.000174) (0.000185)

Decile 7 2.239*** 2.022*** 0.216*** -0.0146*** 0.231*** (0.000128) (0.000119) (0.000175) (0.000237) (0.000254)

Decile 8 2.531*** 2.270*** 0.262*** -0.0309*** 0.293*** (9.59e-05) (0.000447) (0.000457) (0.000170) (0.000447)

Decile 9 2.970*** 2.792*** 0.178*** -0.177*** 0.355*** (0.000464) (0.000630) (0.000782) (0.000762) (0.000965)

Decile 10 4.744*** 4.446*** 0.297*** -0.0673*** 0.365*** (0.00137) (0.000869) (0.00162) (0.00232) (0.00286)

Standard errors in parentheses

*** p

16

Table 2 – Input-Output Simulation Results by Sector

Simulation 1 - Price effect Simulation 2 - Income effect

Sector* Prices

(% change)

Production

(% change)

Employment

(number of jobs)

Prices

(% change)

Production

(% change)

Employment

(number of jobs)

1 1.47 -1.45 -88,190 0.00 3.46 210,238

2 2.00 -1.96 -126,048 0.00 4.44 284,942

3 2.30 -2.25 -21,221 0.00 4.45 41,915

4 1.03 -1.02 -1,502 0.00 1.43 2,093

5 0.81 -0.80 -566 0.00 3.04 2,140

6 0.62 -0.62 -346 0.00 0.25 141

7 1.53 -1.51 -529 0.00 1.03 360

8 2.82 -2.74 -18,550 0.00 5.06 34,245

9 1.54 -1.52 -3,530 0.00 3.00 6,984

10 2.63 -2.56 -32,859 0.00 4.95 63,609

11 1.59 -1.56 -2,819 0.00 6.08 10,954

12 3.66 -3.53 -677 0.00 3.59 689

13 8.89 -8.16 -54,134 0.00 5.45 36,170

14 9.11 -8.35 -151,242 0.00 6.03 109,314

15 4.62 -4.42 -24,466 0.00 5.52 30,565

16 2.79 -2.71 -11,525 0.00 2.63 11,169

17 1.95 -1.91 -3,928 0.00 3.26 6,713

18 2.13 -2.09 -4,349 0.00 3.95 8,236

19 1.23 -1.22 -318 0.00 4.10 1,072

20 1.92 -1.88 -1,746 0.00 4.03 3,738

21 1.17 -1.16 -1,124 0.00 2.77 2,685

22 1.37 -1.36 -1,366 0.00 2.55 2,571

23 2.70 -2.63 -3,962 0.00 4.84 7,289

24 1.78 -1.75 -1,842 0.00 4.44 4,684

25 2.58 -2.52 -12,756 0.00 3.27 16,574

26 1.52 -1.49 -10,363 0.00 1.22 8,454

27 0.99 -0.98 -1,447 0.00 1.39 2,047

28 1.46 -1.44 -1,688 0.00 1.56 1,835

29 1.41 -1.39 -10,955 0.00 2.30 18,184

30 1.77 -1.74 -3,223 0.00 3.18 5,876

31 1.88 -1.84 -4,898 0.00 2.67 7,113

32 1.62 -1.59 -7,951 0.00 0.59 2,936

33 1.56 -1.54 -3,224 0.00 2.83 5,922

34 1.83 -1.80 -6,230 0.00 2.27 7,874

35 2.54 -2.48 -3,323 0.00 1.65 2,204

36 2.64 -2.57 -21,453 0.00 4.04 33,704

37 1.21 -1.19 -6,636 0.00 2.28 12,687

38 0.92 -0.91 -1,336 0.00 4.57 6,726

39 1.71 -1.68 -10,217 0.00 3.74 22,701

40 0.85 -0.84 -74,135 0.00 0.18 15,480

41 1.34 -1.32 -37,366 0.00 4.01 113,477

42 3.41 -3.30 -519,418 0.00 4.05 638,916

43 1.26 -1.24 -45,671 0.00 4.18 153,688 (continues on the next page)

17

(Table 2 – Input-Output Simulation Results)

Simulation 1 - Price effect Simulation 2 - Income effect

Sector Production (%

change)

Prices (%

change)

Employment

(number of jobs)

Prices

(% change)

Production (%

change)

Employment

(number of jobs)

44 2.16 -2.11 -1,288 0.00 3.00 1,825

45 4.72 -4.51 -3,045 0.00 3.61 2,439

46 1.51 -1.49 -12,375 0.00 3.76 31,285

47 3.41 -3.30 -13,644 0.00 3.15 13,026

48 4.60 -4.40 -204,706 0.00 5.68 264,586

49 3.54 -3.42 -5,742 0.00 4.75 7,966

50 2.43 -2.37 -4,313 0.00 4.12 7,484

51 1.95 -1.91 -4,777 0.00 5.38 13,462

52 2.06 -2.01 -14,140 0.00 1.60 11,226

53 3.58 -3.46 -38,871 0.00 4.58 51,475

54 0.23 -0.23 -904 0.00 5.96 23,338

55 3.87 -3.73 -60,406 0.00 3.47 56,234

56 3.47 -3.36 -19,793 0.00 1.66 9,764

57 4.13 -3.97 -20,522 0.00 3.80 19,625

58 2.24 -2.19 -7,353 0.00 3.02 10,132

59 5.34 -5.07 -207,178 0.00 2.69 110,038

60 0.93 -0.92 -7,832 0.00 2.84 24,159

61 4.80 -4.58 -251,073 0.00 0.21 11,310

62 8.90 -8.17 -349,012 0.00 0.04 1,693

63 10.51 -9.51 -220,767 0.00 6.03 140,094

64 6.34 -5.96 -109,680 0.00 0.07 1,294

65 5.54 -5.25 -136,644 0.00 4.69 122,129

66 6.08 -5.73 -53,164 0.00 4.23 39,177

67 6.39 -6.00 -238,301 0.00 4.06 161,272

68 11.31 -10.16 -667,806 0.00 6.41 421,424 *Sectorial names can be found in Annex 1.

Source: Prepared by the authors

18

Table 3 – Input-Output Simulation Results by Decile

Initial Consumption

(BR$)

Simulation 1 - Price

effect

Simulation 2 -

Income effect Total

Decile 1 64,032.19 -1,580.78 1,451.16 -129.62

Decile 2 82,708.60 -2,098.86 1,474.98 -623.88

Decile 3 98,797.43 -2,596.04 2,283.05 -312.99

Decile 4 113,944.09 -3,051.55 3,302.34 250.79

Decile 5 138,811.42 -3,858.31 4,502.10 643.79

Decile 6 170,131.59 -4,759.55 5,339.18 579.63

Decile 7 211,435.99 -6,163.38 8,119.61 1,956.22

Decile 8 274,868.33 -8,257.10 11,328.93 3,071.83

Decile 9 402,624.86 -12,192.06 18,115.83 5,923.77

Decile 10 1,231,657.01 -39,627.70 31,144.27 -8,483.43

Total 2,789,011.50 -84,185.33 87,061.44 2,876.11

Source: Prepared by the authors

Table 4 – Aggregated Input-Output Simulation Results

Simulation 1 - Price

effect

Simulation 2 - Income

effect Total

Production (% change) -2.77% 3.22% 0.36%

Employment (number of jobs) -3,992,464 3,515,372 -477,092

GPI (% change) 2.90% 0.00% 2.90%

Welfare (BR$) - 84,185.33 87,061.44 2,876.11

Source: Prepared by the authors

19

Annex 1 – Sectors description

Sector Code Description

1 Agriculture, forestry, logging

2 Livestock and fisheries

3 Oil and natural gas

4 Other mining and quarrying

5 Food and drinks

6 Smoke products

7 Food & Beverage Outlets

8 Clothing articles and accessories

9 Leather and shoe artifacts

10 Wood Products - exclusive furniture

11 Pulp and paper products

12 Newspapers, magazines, nightclubs

13 Oil refining and coke

14 Alcohol

15 Chemicals

16 Perfumery, hygiene and cleaning

17 Rubber & Plastics

18 Non-metallic mineral products

19 Basic Metallurgy

20 Metal products - exclusive machinery and equipment

21 Machinery and equipment, comprehensive maintenance and repairs

22 Home appliances

23 Office machines and computer equipment

24 Electrical machinery, apparatus and equipment

25 Electronic material and communications equipment

26 Medical apparatus and instruments

27 Vehicles, trailers and buses

28 Parts and accessories for motor vehicles

29 Other transportation equipment

30 Furniture and decorations, garden

31 Electricity and gas, water, sewage and urban cleaning

32 Construction

33 Trade

34 Transportation, paper and packaging

35 Information services

36 Financial intermediation and insurance

37 Real estate services and rentals

38 Maintenance and repair services

39 Accommodation and food services

40 Business services

41 Merchant education

42 Health and Safety

43 Other services

44 Public education

45 Public health

46 Public administration and social security